A partial Padé-via-Lanczos method for reduced-order modeling

The classical Lanczos process can be used to efficiently generate Padé approximants of the transfer function of a given single-input single-output time-invariant linear dynamical system. Unfortunately, in general, the resulting reduced-order models based on Padé approximation do not preserve the stability, and possibly passivity, of the original linear dynamical system. In this paper, we describe the use of partial Padé approximation for reduced-order modeling. Partial Padé approximants have a number of prescribed poles and zeros, while the remaining degrees of freedom are used to match the Taylor expansion of the original transfer function in as many leading coefficients as possible. We present an algorithm for computing partial Padé approximants via suitable rank-1 updates of the tridiagonal matrices generated by the Lanczos process. Numerical results for two circuit examples are reported.